No gameplay out of the box. Requires to find the drive image to mount it manually.

Watch intro video from game folder, loop-mount USB stick image
Broken audio in intro video; skip it and watch TUSFitG.mp4
from the game folder.
There is practically no gameplay in the usual sense, it's all about digging through a stranger's private data. The game itself is just a window asking for three passwords to unlock three achievements, which works fine with Proton.
Accessing the file system requires a little tinkering. You can either loop-mount the image as root (see previous reports) or simply open it with Gnome's "Disk Image Mounter" application. Given that the entire game is really about tinkering that seems quite acceptable. I don't believe you're missing out on any content.

Image doesn't auto mount
You can mount the image using
sudo mount $(sudo losetup --show -f ~/.steam/steam/steamapps/common/TUSFitG/TUSFitG.VHD) /mnt
To unmount use
sudo umount /mnt
sudo losetup -d /dev/loop0 # Loop number may be different (check with mount -l)

Does not automatically mount the USB image
Mounted the USB stick manually via guestmount
You're still able to mount it manually, though - the image is saved in the common directory and can be mounted via guestmount from libguestfs-tools

Launched page saying you'll be asked to mount a USB device.
Also tried with Proton GE
No such prompt existed and the following non-first-launch was fully borked...